[FRIAM] Celeste Kidd - How to Know

[Marcus Daniels]

W. F. Donkin wrote:

"When several hypotheses are presented to our mind which we believe to be mutually exclusive and exhaustive, but about which we know nothing further, we distribute our belief equally among them .... This being admitted as an account of the way in which we actually do distribute our belief in simple cases, the whole of the subsequent theory follows as a deduction of the way in which we must distribute it in complex cases if we would be consistent."

In another context, Eric mentioned the concept of branching structures.   In mixed integer branch & cut solvers, the decisions concerning how to repeatedly separate a problem into sub-spaces is one of the most crucial to get right.   There's a significant literature on it.   Some involve lookahead, others use information theoretic techniques, others do aggregation of variables into simpler forms.   Which one works the best, as far as I can tell, is problem dependent.   It is some analogue to No Free Lunch, I suspect.   It is not unreasonable for a solver to compete them, given the compute resources, however the conclusion from that competition should not be that one policy is better than the other.   Also it reminds me of Glens' advocacy of parallax.

Marcus
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